*In this Q&A with Dr. Matt Larson, a former math teacher and current President Elect of The National Council of Teachers of Mathematics, HMH takes a closer look at the opportunity gap in mathematics and how effective tracking and assessments are.*

**1. Can you explain the “gap” in math learning? What is the difference between an achievement gap and an instructional gap?**

The best measure we have of mathematics achievement in the United States is the National Assessment of Educational Progress (NAEP). It is generally agreed that the NAEP assessments, administered every two years in grades 4, 8, and 12, are valid and reliable. Looking at the scores from 1990 to 2015 reveals that at both the elementary and middle levels, the long-term trend in NAEP scores has been positive and students have made significant progress since 1990.

Although mean NAEP scores for high school students have been essentially flat since 1973, both the mean SAT and ACT mathematics scores increased between 1990 and 2015, with a record number of test takers in 2015. The challenge for us as educators is that although all subgroups of students have improved their performance on the NAEP and that learning differentials have narrowed since 1990, significant learning differentials between different groups of students remain.

It is important to note that I referred to “learning differentials” and not the “achievement gap.” One of the problems with the phrase “achievement gap” is that when it is used some people interpret it to mean that the student is to blame for the gap. On the other hand, if we refer to the “instructional gap” or “opportunity gap,” then the responsibility is clearly on us as educators to address the learning opportunities we provide students that lead to learning differentials.

**2. A lot of attention is given to scores and testing. Why are math scores important and what do they tell educators? **

Mathematics learning outcomes must not be solely viewed through the lens of test results; they must also be seen through the lens of experience. Learning outcomes are in large part a function of how students experience mathematics learning, participate, and are motivated by their individual agencies and identities. For teachers, one key point is that they must help students see themselves as capable of learning and using math.

Much of the focus of assessment in mathematics teaching and learning is on end of the year tests used for accountability purposes. Traditionally the purpose of assessment has been for “grading and rating.” Once again, the focus has been on the student. To be effective, we must use math scores as an integral tool of instruction and use the results to inform our instructional decisions and program improvement. We must focus more on the results of classroom-based assessments and view those results as a reflection on how effective we have been in the classroom, how students have experienced mathematics in the classroom, and the opportunities we have provided students.

**3. How can educators narrow this opportunity gap? There obviously isn’t a one-size-fits-all solution; do you have any general suggestions for educators?**

In order to close the opportunity gap in math, we must address structural obstacles, such as tracking, that stand in the way of students having access to meaningful instruction. Two of these obstacles are tracking and the use of assessment.

Although tracking is often viewed as a secondary concern, the reality is that “tracks” in mathematics are often established as early as the primary grades when students who struggle in kindergarten are placed in a “low” mathematics group in first grade. Once placed in these low instructional groups, it is very difficult for students to move to an on-grade level group.

The problem is that students in high or grade-level groups typically have access to new mathematical ideas, concepts, and problem solving, whereas students in low-groups tend to repeat the same basic computational skills, putting them further behind their peers in grade-level groups. However, when these students are given access to grade-level curriculum and appropriate support, evidence shows that they are more than capable of learning the material and catching up.

**4. Do you think narrowing/closing the gap in mathematics is an obtainable goal? **

If we think we have an instructional gap versus an achievement gap, then not only can we close it, but we must. We need to recognize that we have a moral obligation to remove instructional obstacles to ensure that each and every student has the opportunity and experiences necessary to learn at high levels.

I will not be satisfied with student achievement in the United States until learning differentials associated with demographic factors completely disappear. We live in a world where mathematics is increasingly used to characterize societal problems and formulate solutions. Without strong quantitative skills and a positive mathematics identity and sense of agency, members of our society will find it increasingly difficult to participate in our society.